derivative ((x+1)^2)/((3x-4))

解

導関数

\frac{( x + 1 ) ^{2}}{( 3 x - 4 )}

\frac{3 x ^{2} - 8 x - 11}{( 3 x - 4 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{( x + 1 ) ^{2}}{3 x - 4})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ( x + 1 ) ^{2} ) ( 3 x - 4 ) - \frac{d}{d x} ( 3 x - 4 ) ( x + 1 ) ^{2}}{( 3 x - 4 ) ^{2}}

\frac{d}{d x} ((x + 1)^{2}) = 2 (x + 1)

\frac{d}{d x} (3 x - 4) = 3

= \frac{2 ( x + 1 ) ( 3 x - 4 ) - 3 ( x + 1 ) ^{2}}{( 3 x - 4 ) ^{2}}

拡張

2 (x + 1) (3 x - 4) - 3 (x + 1)^{2} : 3 x^{2} - 8 x - 11

= \frac{3 x ^{2} - 8 x - 11}{( 3 x - 4 ) ^{2}}